According to the law of refraction, namely \(n_1 \sin \phi _1=n_2\sin \phi _2\)  with \(n\)  the index of refraction and \(\phi \)  the angle to normal direction, we know that the threshold angle for total reflection (\(\phi _2=\pi /2\) ) is \(\phi _1=\textrm {arcsin}~(n_2/n_1)\) . Referring to the definition of \(n\)  (\(n=c/v_{ph}\)  or \(n=\lambda _0/\lambda \)  with \(c\)  the speed of light, \(v_{ph}\)  the phase velocity, and \(\lambda _0\)  the wavelength in vacuum) and waves in uniform magnetised plasma[1]}, [2]}, we can write \(n\)  in form of

\(n^2=\frac{G\pm F}{2(\varepsilon \sin ^2\psi +\eta \cos ^2\psi )}\) 
